Although great progresses has been made in the understanding of
quantum phase transition from the fundamental principles of quantum
mechanics, an important question is not yet resolved: whether there
exists a universal way to characterize the different phases and
their boundaries. More specifically, could the geometric phase of
the ground state in many-body systems serve this purpose? This
conjecture is natural since the quantum phase transition generally
emerges from the degeneracy of the ground state in many-body
systems. Geometric phase as a measurement of the curvature of the
Hilbert space, could mark the fantastic changes of the ground state
when degeneracy happens. However the critical point is how to obtain
the geometric phase of the ground state. The earlier method is to
impose a local rotation about some special orientations, as has been
done in [1]}, [2]}, [3]}. In our own viewpoints, the
connection built by this method is fragile; the geometric phase is
trivial when the system is symmetrical about this rotation.
